3x-17+3x^2=-4

Solution for 3x-17+3x^2=-4 equation:

3x-17+3x^2=-4

We move all terms to the left:

3x-17+3x^2-(-4)=0

We add all the numbers together, and all the variables

3x^2+3x-13=0

a = 3; b = 3; c = -13;
Δ = b2-4ac
Δ = 32-4·3·(-13)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{165}}{2*3}=\frac{-3-\sqrt{165}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{165}}{2*3}=\frac{-3+\sqrt{165}}{6}
$